Yes it is possible to pull the injector to get the busted pieces out,using needle nosed pliers,bubble gum on a stick,or a shop vac,etc--but be aware on an older engine,the fuel lines will likely be rusty and pitted,and may not survive being disturbed...also its very easy to snap off the return line nipples on an injector ,if the socket tilts or slips while your loosening it..
Neither the fuel lines or injectors are cheap ,and good used ones are hard to find,especially in the rust belt states..
I've had one glow plug break while the engine was running in my pickup--it clattered like a bad lifter for several miles,after I first heard the noise and determined it still had good oil pressure,I decided to just drive it the 4 miles home...sounded awful!..
But I did get home,and when I was close enough to walk the rest of the way,I dropped it in first and floored it until it hit the govenor limits--figured it would either blow up--or blow out the glow plug bits...it quieted down after that,so I'm assuming it just blew the chunks out the exhaust..from that day on I hear a lifter tap noise till the engine warms up good after a cold start..may have bent a pushrod slighty or some other valve train part..but it runs the same..
The engine seems no worse for the wear,but I wouldn't doubt the cylinder or valves could well have suffered some trauma..
I read stories online about Humvees having them snap off,and the army mechanics simply started the engine and revved it up to blow out the chunks,with no apparent damage,but I wouldn't want to try it..also read where some tried leaving the plugs unscrewed that had mushroomed tips,and ran the engine to let the compression and heat blow them out like bullets....that sounds risky too..

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After I replaced that plug that failed I noticed half of it was gone,and it was an Autolite 1110 plug,the rest were AC 60G --one diesel mechanic I asked said he's seen more than one plug fail like that and it could be "mixing" different brands or part numbers.like 60G's and 9g's might send more current to the "oddball" and cause it to burn up--also said he would not use 9G or other stock glow plugs with a manual override either,they are almost sure to mushroom and cause grief when its time to remove them..
I've had to replace my glow plugs 3 times in 12 years,they ROT AWAY before they fail electrically in most cases--had to toss several "good" ones out because I was afraid I wouldn't be able to get them OUT later,the 3/8 "hex was whittled away to nothing,I had to hammer a 5/16" 6 point socket on them to get them loose!--was afraid I wouldn't be able to grip them,or snap the hex off the body of the plug...that would suck if it happened on the rear most cylinders you cant get at easily...